Stretchable interconnects are essential structures in stretchable electronics. Typically, these structures are formed by metal conductors of different shapes on top of or encapsulated within a rubber material. Interfacial delamination during elongation is one of the major failures affecting the elasticity of interconnects. Stress concentration on substrate is the source of delamination. This study uses a numerical model of stretchable interconnects to analyze stress concentration phenomenon of typical structure shapes: the horseshoe, the zigzag, the U shape and the rectangle shape. The simulation is implemented by commercial finite element analysis software, ABAQUS. The simulation results demonstrate that stress concentrate area is larger at the edge of larger arc when out of plane deformation of the metal lines is small. However the geometrical configuration of the metal line shape has little effect on delamination. The phenomenon which found in this study cannot be ignored when designing metal line layouts.